This was me last year!
I had a rat in my kitchen too, despite having a jack russell. I called the council out and they put trays of rat poison in the back of my fridge, well behind it, as that's where the bugger had been chewing the insulation to make its bedding with.
It took several weeks of him coming out, redoing the poison, but it disappeared eventually- dunno where, don't care, but we never found it.